Frustration and Whining
When I have a 3- or 4-year-old who gets frustrated easily or resorts to whining, the first thing is to take your own blood pressure—meaning the calmer you guys are in responding, the less she will see that increasing tone or volume or urgency does not necessitate an emergency on your part.
At 3, I like the 3-Strikes-and-I-Am-In rule, and at 4, the 4-Strikes-and-I-Am-in Rule. If a kiddo is getting frustrated and asking or whining for help, I'll first say, “Oh that looks tough! Can you tell me what is going on in a normal voice so I can hear you better?” And then, once a normal tone is used, I will give some vague but helpful direction so she can try a new approach. I will do this 3 times before I go down and sit and do hands-on teaching (and also make sure we aren't doing something like a puzzle made for 10-year-olds). Then, when I show them how to do it or approach it differently, I put the pieces or activity back to how I found it (not finished) so they can try it themselves.
Provide good feedback for things that they are working hard to accomplish and not just note, “Oh, hey, the puzzle looks great. Good job!” But more like “The puzzle looks great! I know that is hard to do because of this tricky part here and look you figured it out all on your own! How does that make you feel?”
Also, I want them to see you guys struggle with something and work through it. Like if you are trying to open a jar and can't open it, ask them to come over and ask what they would do so they are really engaged; then, you keep working at it. If you open the jar, they see how grit is good. If you don't open the jar, they see how you deal with frustration in a healthy way, such as trying later or asking for help in a calm and specific way.
As for general whining, I always go with, “Oh, I think you are asking for help with something, but it is hard to hear when you are saying it that way. Can you try a different way?” And if they freak out when asked to repeat themselves, you can just ignore the whining until they calm down and then ask if they still need help. Almost like an older version of dealing with the terrible twos.